H 2-H∞ Control of Discrete Time Nonlinear Systems Using the SDRE Approach

A novel H2–H∞ State Dependent Riccati Equation control approach is presented for providing a generalized control framework to discrete time nonlinear system. By solving a generalized Riccati Equation at each time step, the nonlinear state feedback control solution is found to satisfy mixed performance criteria guaranteeing quadratic optimality with inherent stability property in combination with H∞ type of disturbance attenuation. Two numerical techniques to compute the solution of the resulting Riccati equation are presented: The first one is based on finding the steady state solution of the difference equation at every step and the second one is based on finding the minimum solution of a linear matrix inequality. The effectiveness of the proposed techniques is demonstrated by simulations involving the control of an inverted pendulum on a cart, a benchmark mechanical system.

Influence of Leaders on Mean Square Consentability in Biologically-Inspired Stochastic Networks

In this work, we study a discrete-time consensus protocol for a group of agents which communicate over a class of stochastically switching networks inspired by fish schooling. The network model incorporates the phenomenon of numerosity that has a prominent role on the collective behavior of animal groups by defining the individuals’ perception of numbers. The agents comprise leaders, which share a common state, and followers, which update their states based on information exchange among neighboring agents. We write a closed form expression for the asymptotic convergence factor of the protocol, which measures the decay rate of disagreement among the followers’ and the leaders’ states. Numerical simulations are conducted to validate analytical results and illustrate the consensus dynamics as a function of the group size, number of leaders in the group, and the numerosity.

Design and Control of a Compact and Flexible Pneumatic Artificial Muscle Actuation System: Part Two—Robust Control

A robust control approach is presented in this part of the paper, which provides an effective servo control for the novel PAM actuation system presented in Part I. Control of PAM actuation systems is generally considered as a challenging topic, due primarily to the highly nonlinear nature of such system. With the introduction of new design features (variable-radius pulley and spring-return mechanism), the new PAM actuation system involves additional nonlinearities (e.g. the nonlinear relationship between the joint angle and the actuator length), which further increasing the control difficulty. To address this issue, a nonlinear model based approach is developed. The foundation of this approach is a dynamic model of the new actuation system, which covers the major nonlinear processes in the system, including the load dynamics, force generation from internal pressure, pressure dynamics, and mass flow regulation with servo valve. Based on this nonlinear model, a sliding mode control approach is developed, which provides a robust control of the joint motion in the presence of model uncertainties and disturbances. This control was implemented on an experimental setup, and the effectiveness of the controller demonstrated by sinusoidal tracking at different frequencies.

Nonlinear Robust H∞ Control With State-Dependent Scaling

This paper addresses the design of nonlinear robust H∞ controllers for nonlinear uncertain systems with polynomial vector field and norm bounded uncertainties. We derive state-dependent matrix inequalities, using Lyapunov’s direct method, that stabilize the nonlinear systems and guarantee robust performance using nonlinear state-feedback control. The state-dependent synthesis conditions incorporate state-dependent scaling to minimize the ℒ2 gain of the disturbance/output. Sum-of-squares (SOS) optimization is applied to solve the resulting synthesis condition with optimized ℒ2 gain for the nonlinear system, without requiring an iterative approach. Finally, a design example of nonlinear Van der Pol equation is presented.

Stabilization of Nonlinear Strict-Feedback Systems With Time-Varying Delayed Integrators

We consider nonlinear systems in the strict-feedback form with simultaneous time-varying input and state delays, for which we design a predictor-based feedback controller. Our design is based on time-varying, infinite-dimensional backstepping transformations that we introduce, to convert the system to a globally asymptotically stable system. The solutions of the closed-loop system in the transformed variables can be found explicitly, which allows us to establish its global asymptotic stability. Based on the invertibility of the backstepping transformation, we prove global asymptotic stability of the closed-loop system in the original variables. Our design is illustrated by a numerical example.

An E/H Control Design for a Hydraulic Variable Displacement Axial Piston Motor

A simple and novel speed control scheme for variable displacement motors has been developed under the consideration of some system uncertainties. Theoretical analysis and experimental test results have shown that the proposed control strategy is capable of driving the swashplate to track its desired trajectory with robust stability and satisfactory performance. An adaptive learning algorithm enables the controls to automatically adjust for uncertainties in the control bias current. Compared with its hydro-mechanical counterpart, the provided E/H control results in a hydraulic variable displacement motor with lower cost and better performance.

Position-Mode Haptic-Based Control of Teleoperated Hydraulic Actuators

A control scheme for teleoperation of hydraulic actuators, using a haptic device, is developed and experimentally evaluated in this paper. In the control laws, the position error between the displacement of the haptic device and the hydraulic actuator movement is used at both master and slave sides to maintain good position tracking at the actuator side while providing a haptic force to the operator. Lyapunov’s stability theory and LaSalle’s invariant set theorems are employed to prove the asymptotic stability of the system. It is shown that beside stability, the system performs well in terms of position tracking of the hydraulic actuator and providing a feel of telepresence to the operator. Proposed controller only needs system’s pressures and displacements that are easy to obtain via on-line measurements. Additionally, the controller does not need any information about the parameters of the system. These characteristics make the controller very attractive from the implementation view point.

Optimal Control for the Series-Parallel Displacement Controlled Hydraulic Hybrid Excavator

In this paper a hydraulic hybrid system architecture for multi-actuator displacement controlled systems is analyzed. In particular the problem of optimal control for a hybrid excavator with four actuators is solved. The system states and controls are identified and classified into those which are cycle defined and those which are free to vary during the duty cycle. A state space model is derived for the hybrid system using the free states and controls and an outline of the algorithm used to apply dynamic programming to the system is described. The optimal controls and states for an aggressive truck loading cycle of the excavator are compared with suboptimal controls and states obtained using a rule based control strategy. Finally a comparison is made for the simulated fuel consumption of the system using optimal and suboptimal controls. A comparison is also made between the fuel consumption of the hybrid and non-hybrid excavators.

Optimal Asymptotic Entrainment of Phase-Reduced Oscillators

We derive optimal periodic controls for entrainment of a self-driven oscillator to a desired frequency. The alternative objectives of minimizing power and maximizing frequency range of entrainment are considered. A state space representation of the oscillator is reduced to a linearized phase model, and the optimal periodic control is computed from the phase response curve using formal averaging and the calculus of variations. Computational methods are used to calculate the periodic orbit and the phase response curve, and a numerical method for approximating the optimal controls is introduced. Our method is applied to asymptotically control the period of spiking neural oscillators modeled using the Hodgkin-Huxley equations. This example illustrates the optimality of entrainment controls derived using phase models when applied to the original state space system.

Analysis of an Adaptive Iterative Learning Algorithm for Freeway Ramp Flow Imputation

We present an adaptive iterative learning based flow imputation algorithm, to estimate missing flow profiles in on ramps and off ramps using a freeway traffic flow model. We use the Link-Node Cell transmission model to describe the traffic state evolution in freeways, with on ramp demand profiles and off ramp split ratios (which are derived from flows) as inputs. The model based imputation algorithm estimates the missing flow profiles that match observed freeway mainline detector data. It is carried out in two steps: (1) adaptive iterative learning of an “effective demand” parameter, which is a function of ramp demands and off ramp flows/ split ratios; (2) estimation of on ramp demands/ off ramp split ratios from the effective demand profile using a linear program. This paper concentrates on the design and analysis of the adaptive iterative learning algorithm. The adaptive iterative learning algorithm is based on a multi-mode (piecewise non-linear) equivalent model of the Link-Node Cell transmission model. The parameter learning update procedure is decentralized, with different update equations depending on the local a-priori state estimate and demand estimate. We present a detailed convergence analysis of our approach and finally demonstrate some examples of its application.